多标签分类

1. 算法

多标签分类的适用场景较为常见，好比，一份歌单可能既属于标签旅行也属于标签驾车。有别于多分类分类，多标签分类中每一个标签不是互斥的。多标签分类算法大概有两类流派：

• 采用One-vs-Rest（或其余方法）组合多个二分类基分类器；
• 改造经典的单分类器，好比，AdaBoost-MH与ML-KNN。

One-vs-Rest

基本思想：为每个标签\(y_i\)构造一个二分类器，正样本为含有标签\(y_i\)的实例，负样本为不含有标签\(y_i\)的实例；最后组合N个二分类器结果获得N维向量，可视做为在多标签上的得分。我实现一个Spark版本MultiLabelOneVsRest，源代码见mllibX。

AdaBoost-MH

AdaBoost-MH算法是由Schapire（AdaBoost算法做者）与Singer提出，基本思想与AdaBoost算法相似：自适应地调整样本-类别的分布权重。对于训练样本\(\langle (x_1, Y_1), \cdots, (x_m, Y_m) \rangle\)，任意一个实例 \(x_i \in \mathcal{X}\)，标签类别\(Y_i \subseteq \mathcal{Y}\)，算法流程以下：

其中，\(D_t(i, \ell)\)表示在t次迭代实例\(x_i\)对应标签\(\ell\)的权重，\(Y[\ell]\)标识标签\(\ell\)是否属于实例\((x, Y)\)，若属于则为+1，反之为-1（增长样本标签的权重）；即

\[ Y[\ell] = \left \{ { \matrix { {+1} & {\ell \in Y} \cr {-1} & {\ell \notin Y} \cr } } \right. \]

\(Z_t\)为每一次迭代的归一化因子，保证权重分布矩阵\(D\)的全部权重之和为1，

\[ Z_t = \sum_{i=1}^{m} \sum_{\ell \in \mathcal{Y}} D_{t}(i, \ell) \exp \large{(}-\alpha_{t} Y_i[\ell] h_t(x_i, \ell) \large{)} \]

ML-KNN

ML-KNN (multi-label K nearest neighbor)基于KNN算法，已知K近邻的标签信息，经过最大后验几率（Maximum A Posteriori）估计实例\(t\)是否应打上标签\(\ell\)，

\[ y_t(\ell) = \mathop{ \arg \max}_{b \in \{0,1\}} P(H_b^{\ell} | E_{C_t(\ell)}^{\ell} ) \]

其中，\(H_0^{\ell}\)表示实例\(t\)不该打上标签\(\ell\)，\(H_1^{\ell}\)则表示应被打上；\(E_{C_t(\ell)}^{\ell}\) 表示实例\(t\)的K近邻中拥有标签\(\ell\)的实例数为\(C_t(\ell)\)。上述式子可有贝叶斯定理求解：

\[ y_t(\ell) = \mathop{ \arg \max}_{b \in \{0,1\}} P(H_b^{\ell}) P(E_{C_t(\ell)}^{\ell} | H_b^{\ell} ) \]

上面两项计算细节见论文[2].

2. 实验

AdaBoost.MH算法Spark实现见sparkboost，scikit-multilearn实现ML-KNN算法。我在siam-competition2007数据集上作了几个算法的对比实验，结果以下：

算法	Hamming loss	Precision	Recall	F1 Measure
LR+OvR	0.0569	0.6252	0.5586	0.5563
AdaBoost.MH	0.0587	0.6280	0.6082	0.5837
ML-KNN	0.0652	0.6204	0.6535	0.5977

此外，Mulan提供了众多数据集，Kaggle也有多标签分类的比赛WISE 2014。

实验部分代码以下：

import numpy as np
from sklearn import metrics
from sklearn.datasets import load_svmlight_file
from sklearn.linear_model import LogisticRegression
from sklearn.multiclass import OneVsRestClassifier
from sklearn.preprocessing import MultiLabelBinarizer

# load svm file
X_train, y_train = load_svmlight_file('tmc2007_train.svm', dtype=np.float64, multilabel=True)
X_test, y_test = load_svmlight_file('tmc2007_test.svm', dtype=np.float64, multilabel=True)

# convert multi labels to binary matrix
mb = MultiLabelBinarizer()
y_train = mb.fit_transform(y_train)
y_test = mb.fit_transform(y_test)

# LR + OvR
clf = OneVsRestClassifier(LogisticRegression(), n_jobs=10)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)

# multilabel classification metrics
loss = metrics.hamming_loss(y_test, y_pred)
prf = metrics.precision_recall_fscore_support(y_test, y_pred, average='samples')


"""
ML-KNN for multilabel classification
"""
from skmultilearn.adapt import MLkNN

clf = MLkNN(k=15)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)

// AdaBoost.MH for multilabel classification
val labels0Based = true
val binaryProblem = false

val learner = new AdaBoostMHLearner(sc)
learner.setNumIterations(params.numIterations) // 500 iter
learner.setNumDocumentsPartitions(params.numDocumentsPartitions)
learner.setNumFeaturesPartitions(params.numFeaturesPartitions)
learner.setNumLabelsPartitions(params.numLabelsPartitions)
val classifier = learner.buildModel(params.input, labels0Based, binaryProblem)

val testPath = "./tmc2007_test.svm"
val numRows = DataUtils.getNumRowsFromLibSvmFile(sc, testPath)
val testRdd = DataUtils.loadLibSvmFileFormatDataAsList(sc, testPath, labels0Based, binaryProblem, 0, numRows, -1);
val results = classifier.classifyWithResults(sc, testRdd, 20)

val predAndLabels = sc.parallelize(predLabels.zip(goldLabels)
  .map(t => {
    (t._1.map(e => e.toDouble), t._2.map(e => e.toDouble))
  }))
val metrics = new MultilabelMetrics(predAndLabels)

3. 参考文献

[1] Schapire, Robert E., and Yoram Singer. "BoosTexter: A boosting-based system for text categorization." Machine learning 39.2-3 (2000): 135-168.
[2] Zhang, Min-Ling, and Zhi-Hua Zhou. "ML-KNN: A lazy learning approach to multi-label learning." Pattern recognition 40.7 (2007): 2038-2048.
[3] 基于PredictionIO的推荐引擎打造，及大规模多标签分类探索.